Talk:Coherence (physics)

The main problem with this article is that it is incoherent! Rnt20 10:39, 14 Jun 2005 (UTC)

I have begun a significant rewrite of this article along with new figures. My plan is to start with the broadest possible introduction to coherence. Then give examples of where it can be used. Then examples of types of coherence: temporal, spatial and polarization. Finally, I will end with quantum coherence. Over the coming weeks I will incorporate text from the current page and write the above sections. For now, the article is at http://en.wikipedia.org/wiki/User:J_S_Lundeen/Jeff%27s_Sandbox J S Lundeen 3 July 2005 03:42 (UTC)

Okay, I have brought over the version I was constructing. When considering the changes please remember that coherence is a broad subject and not just applicable to light. --J S Lundeen 05:02, 22 January 2006 (UTC)

Comments

The present illustrations need work, since they reinforce a classic set of misconceptions. In truth, light waves do not act like narrow wiggling snakes. The "wiggling snakes" are actually e-field graphs, with the side-to-side motion being the graph of the strength of the e-field ...and not a transverse motion! And since light waves don't act like serrated threads as depicted, light waves cannot mesh together side by side as the illustrations suggest. The GRAPH of the e-field strength is not a light wave: we confuse the graph of e-field strength for a physical transverse motion.

A visual description of coherent versus incoherent light can be illustrated with two-dimensional fluid waves (e.g. photos of water wave patterns produced in ripple tanks.) To explain coherence/incoherence, we really should be using sphere waves or at least plane waves. Wiggly lines only illustrate waves on a rope, and to be accurate we'd have to compare two waves on ONE rope (or better: two plane waves on one water surface.) The present diagrams are essentially comparing waves found on several different ropes. I'll try to come up with some illustrations, watch [1] --Wjbeaty 02:03, Mar 23, 2005 (UTC)

I agree, it's better to have no pictures than misleading ones. And why should the waves in the second pictures be incoherent? They have all the same frequency and the difference of their phases is constant, so they can interfere. --

That's an issue I'm not clear on. Suppose we sequentially reflect some laser light from several frosted screens. Does an "incoherent wave" result? We could call the resulting wave "incoherent" on the grounds that it's not a plane wave or a sphere wave. Such a wave does not create line gratings or bullseye-shaped zoneplates when interfered, and it's useless in most applications requiring coherent light. Or... we could insist that the diffused wave is "coherent" because the phase difference between any two sampled points in the wave is not changing with time. --Wjbeaty 02:03, Mar 23, 2005 (UTC)

I agree. The figure captions were simply wrong -- as mentioned before, several monchromatic waves of exactly the same frequency are always coherent even if there are phase differences (as in the second diagram). The text specifically says that if you delay a truly monochromatic source (change its phase) it is still coherent with the original wave -- see temporal coherence paragraph, which contradicted the second figure caption completely (the caption said the opposite -- that if the phases are different, waves of the same frequency are incoherent). I have changed the captions, because they simply encouraged common misconceptions. I also added some text to emphasize that coherence and monochromaticity are not the same thing -- Young didn't have lasers and yet he produced coherent light beams (from non-monochromatic sunlight). And as far as the frosted screens are concerned, you are talking about reducing the spatial coherence by making the light come from multiple directions -- this doesn't apply to waves on a string which are all moving in exactly the same direction. Rnt20 14:14, 23 May 2005 (UTC)

I disagree. The pictures were a little misleading but the new captions are pointless. You might as well remove the pictures as they stand. I think you guys are missing a few things in your discussion. There are two main types of coherence, spatial and temporal. You seem to be concentrating on spatial coherence as tested in a Young's double-slit and used in Astronomy. But temporal coherence is the important quantity in other interfometers like the Mach-Zehnder. A truly monocromatic source is temporally coherent for all delays but doesn't need to have any spatial coherence at all. The opposite is also true which is why Young's experiment worked with sunlight. So in summary, the pictures were attempting to show temporal incoherence as opposed to spatial incoherence. For temporal coherence, the depiction of light as a squiggly line is sufficient. See degree of coherence for a more mathematical description of both. Still, the article does need some help. J S Lundeen 20:30, 3 Jun 2005 (UTC)

Indeed this is right. Monochromatic light is the most common example of highly temporally-coherent light, and would make a good example of this. Both of the first two figures show monochromatic light, so one could be removed. The text and ideas on this talk page need to be turned into a new article on coherence -- there are a lot of ideas further down. Rnt20 08:11, 4 Jun 2005 (UTC)

Yes, some of those ideas should be incorporated. But I think really, the article should be rewritten with a broader perspective of coherence. Coherence is a very fundamental concept and is used in acoustics, electrical engineering and especially in quantum physics. The article should begin with the broadest clearest introduction of coherence and what areas it is used in. Then the article should discuss specific examples like temporal and spatial coherence. It is only in this broader perspective that one can answer questions like "how close do two frequencies have to be before they are incoherent?" and apply the answer to every type of coherence. I have started writing something but it will take a while to finish. J S Lundeen 21:33, 6 Jun 2005 (UTC)

Other than a few picky details, I am surprised how good the article is.

I am wanting to work in the speckled look of lasers and some LEDs, somehow. That is perhaps the most often seen coherence. Some car tail lights have LEDs that are too uniform in composition, so they look speckley like supermarket lasers. David R. Ingham 20:59, 9 March 2006 (UTC)

Perfect coherent waves

The article doesn't explain in which case two waves are considered coherent and in which case not. For example, imagine two waves of the same frequency, just one billionth of a nanometer apart. are these waves already considered incoherent? I guess there is no laser in the world that exact to produce truly coherent waves of light. Thus, is there a percentage needed for phase relation to consider waves coherent? Thanks, --Abdull 16:36, 30 Mar 2005 (UTC)

By "billionth of a nanometer apart," what do you mean? Since two waves always add together to create a single wave that's weaker or stronger than the originals, in what way can they be "apart?" (If you're talking about the present misleading diagrams, then perhaps you've fallen for the misconception that light can behave like wiggling snakes with a space between the adjacent "snakes." Light acts nothing like this... yet these "wiggling snakes" diagrams appear widely in science articles and textbooks.) --Wjbeaty 05:59, Mar 31, 2005 (UTC)

Snakes, etc.

There is a problem with the pictures in this article, as has been noted. I'm not a real expert in this area, but I'm trying to figure out a better way to present this. As mentioned above, the diagram showing "incoherent" light is not really correct. If the phase relationship between those waves were to remain constant with time, then they would be coherent, as the interference pattern would not change. What we need is a second snapshot at a later time showing a different phase relationship, which would then demonstrate incoherence.

Also, diagrams somehow demonstrating spatial coherence would be good. Gwimpey 00:59, May 14, 2005 (UTC)

By definition, if the phase difference between two monochromatic waves varies with time, they have different frequencies (note that the definition of (angular) frequency is the rate of change of phase with time). So the only incoherent example is the third figure where the wavelengths are different. If the waves are not monochromatic they must each have a different range of frequencies if the waveforms are to vary in a different way with time. I have added some text to explain this.

So by definition, two waves of exactly the same frequency, travelling in exactly the same direction are always fully coherent, regardless of the phase difference between the waves (as shown in the second diagram).

Rnt20 14:22, 23 May 2005 (UTC)

Monochromatic etc.

I think monochromatic means "single frequency". Also I think the concepts of coherence or incoherence only apply to time harmonic waves. Waves with different frequencies can not be coherent, since they can not keep constant phase relationships with one another, thus no constructive or destructive interferences are possible . Monochromatic waves (waves with the same frequency) may be incoherent, provided the phases of the waves are random with each other, like the light from a hot tungsten filament. Please correct me if I am wrong.

Speckle pattern from a binary (double star) taken with the Nordic Optical Telescope. Note how each star has broken up into a pattern of speckles in a Rayleigh distribution.

The first point is a common misconception between temporal coherence (how monochromatic a light is) and the coherence between two or more signals (which is what is most commonly measured with optical instruments). The coherence between two signals is just a measure of how correlated they are to each other, and has nothing to do with their shape (it has nothing to do with whether the signals are sine waves, square waves, or any other shaped wave, like random noise). This is how it is possible for astronomical interferometers to measure the coherence of starlight, without requiring the starlight to consist of a sine wave (and in fact this is true of any imaging system -- the human eye works because white light combines coherently on the retina after passing through the lens, and this works even though the light source (the sun) does not produce pure sine waves -- if this wasn't true we would see uniform illumination in all directions, like a person with a cornea infection). A nice example of coherence is the "speckle pattern" that you get when observing white light from a star through the atmosphere (see image at right). This pattern is a coherence effect (it is a rayleigh speckle pattern) which is more commonly seen when you scatter laser light onto a surface (e.g. the reflection of a laser pointer), but in this case it is produced by many rays of white light combining coherently (to form what we call an image, in this case a speckled image of the star).

Tungsten lamps produce broad-band (non-monochromatic) light. You can filter this light to select a narrow range of wavelengths, and then the light you get will be exactly identical to the light you get from a (faint) laser having the same range of wavelengths (and the same spatial coherence -- i.e. coming from the same range of directions). There is no fundamental difference between the light from a tungsten filament and the light from a laser, apart from the range of frequencies and the angular size of the source typically being different (unless you use filters on the tungsten light to make the range of frequencies and angles the same). The biggest benefit of lasers is that they can be much brighter (and more convenient) than a temporally-coherent light source made using filters like Dennis Gabor's one described in the last paragraph of the article.

If a filtered filament light bulb has only a small range of frequencies (so it is almost, but not perfectly monochromatic), what you get out is a sine wave which varies randomly in phase (and amplitude) with time. The reverse is also true -- if you have a sine wave which varies randomly in phase with time, then by definition it is not monochromatic because a rate of change of phase with time is the same thing as a frequency shift (this is how frequency is actually defined!).

I hope this is helpful. Rnt20 12:02, 24 May 2005 (UTC)

This surely helps, thanks a lot. I understand that the tungsten lights are not monochromatic, what i said was wrong. I read the article and i want to make sure i understand it right. So coherence is a measure of how two signal sources are correlated and it has nothing to do with the shape of the waveform being sinusoidal or not, what do u mean by the word correlated? is it a measure of how similar the two waveforms are to each other, as the term correlation is usually defined? About the temporal coherence, in the article you say that the coherence time of a source is inversely proportional to its bandwidth, i am wondering if the temporal coherence is a different way to say the time duration of the signal or the pulse; It seems to me that u are saying wave sources with the same frequency are always coherent, but what about the phases of these different wave sources related to each other? If I have a filtered tungsten filament which gives out a single frequency light or light has only a small range of frequencies as u wrote above, then do u think the lights from different parts of the tungsten line segment will all be in phase with each other? what about the lights from a thousand such filtered light bulbs? I know nothing about optics or speckle patterns, but i know if a plane wave pass through a random medium, the wave front will develop wiggles and if i have a finite receiving aperture and if i scan the receiver over a plane i will get signal variations, i do a raster scan and i will get a spotty image. is that what u call speckle pattern?

Actually, I wasn't quite right (or not quite clear actually). I think the simplest explanation is probably something like:

If you measure the electromagnetic signal at two places (e.g. with two radio telescopes), and the signals are exactly identical then they are perfectly correlated, and are thus spatially coherent. With radio telescopes astronomers multiply the electric field measured at one telescope with the field measured at another, and then sum the result as a function of time, in a device unimaginatively called a correlator (see VLBI). If there is perfect correlation between the two signals, then the signals are coherent (and so there is spatial coherence between the two points in space). Note again that neither of these signals is necessarily a sine wave (although radio telescopes are normally restricted to a certain bandpass, perhaps covering a few GHz of frequency). Now the signals don't have to be correlated -- for example they could be anti-correlated (one being the opposite of the other) and they would still be coherent. The wave field used to describe electromagnetic waves is usually described in terms of complex numbers, so two anti-correlated signals are 180 degrees out of phase. In fact any other constant phase rotation is allowable, and the signals would still be coherent (actually this is a bit of a simplification, but it's sort-of correct). This is exactly how radio interferometry works for astronomy (again, see VLBI) -- how coherent the signals from the two telescopes are is called the fringe "visibility amplitude", and the average phase offset is called the "visibility phase" (e.g. the visibility phase would be 180 degrees if the signals were anti-correlated, or opposites of each other). Astronomical optical interferometry is the same, but it isn't possible to multiply the optical signals together, so a clever set of intensity measurements is done with different phase shifts, resulting in the same answer as if you'd multiplied the signals (see e.g. http://www.geocities.com/CapeCanaveral/2309/page2.html ).

If you have sine waves at both locations with the same wavelength, then they will be spatially coherent (because they look the same). If there is even the slightest difference in frequency (or any random changes in phase with time) then they won't be coherent with each other.

Now the other case of interest is when you measure the electromagnetic signal twice at the same place, but at two different times. Then you are measuring temporal coherence instead of spatial coherence, but otherwise it is all the same. Now the most common temporally coherent light is monochromatic light (or as monochromatic as you can make it) -- there you have a sine wave which looks the same at one time as it does at a later time, so it is temporally coherent. If the light is not quite monochromatic (the sine wave is changing gradually with time) then the coherence decreases when you reach a time delay corresponding to the "coherence time" of the source, which is inversely proportional to the bandpass (range of wavelengths). Of course a source doesn't have to be a sine wave to be temporally coherent, but it has to be some kind of repeating pattern, and a sine wave is the most obvious (and practically realisable) example. Temporal coherence of light sources is measured using a Michelson, or Fourier transform spectrometer (see http://scienceworld.wolfram.com/physics/FourierTransformSpectrometer.html). This device simply splits a light beam into two, delays one half by a variable length of time, and the recombines the light back into one beam. This allows you to directly measure the temporal coherence for any chosen time delay. This is normally done at a range of time delays, and then the plot of coherence vs time delay is Fourier transformed, which gives a spectrum of the light source (hence the name of this type of instrument).

--J S Lundeen 05:02, 22 January 2006 (UTC)

polarization

The Poincare sphere link does not explain its application to polarization. Does the sphere represent the possible combinations of linear and circular polarization, as well as the degree of polarization? Did Poincare have more than one sphere named for him? David R. Ingham 21:24, 9 March 2006 (UTC)

Your right. There must be two Poincare spheres although it appears they are abstractly related. Yes, a vector in the Poincare sphere represents any combination of linear circular polarization as well the degree of polarization. I'll change the link to something more appropriate.--J S Lundeen 16:04, 10 March 2006 (UTC)

Fourier Theorem and Coherence of Light

I think the article promotes a general misconception about the association of the coherence time of light with the spectral bandwith over the Fourier theorem:

the Fourier theorem assumes actually that all superposing waves are locked in phase: for instance, the frequency spectrum of a rectangular pulse of duration T is given by the sinc-function sin(f*T/2)/(f*T/2) where f is the (angular) frequency. The pulse is exactly reconstructed if one superposes waves (ranging continuously in frequency from -infinity to +infinity) with this amplitude, but this is obviously only possible if all the sub-waves belonging to the individual frequencies f are locked in phase somehow. If the phases of the waves are however randomly uncorrelated, they could never produce the constructive and destructice interference required to reconstitute the rectangular pulse. The point here is that for all natural light sources the phases of the individual waves *are* randomly uncorrelated as they originate from statistically independent atomic emissions (i.e. the 'continuum' of the sun for instance is actually a spectrum consisting of many blended lines). So the Fourier theorem can not be applied here to obtain the coherence time of the signal from the shape of the spectrum. The coherence time is determined physically by the atomic decay times and/or collision times that are relevant for the radiation produced.

In this sense the paragraph about 'white light' in particular is incorrect in my opinion.

Thomas

Hi Thomas

Thanks for your comments. You misunderstanding is a very common one. White light and pulsed light with the same spectral bandwidth have the same coherence time. Coherence time has nothing to do with the phase relationship between different frequencies. Light pulses can not be any shorter than their coherence time, but they can be longer. Obviously, this needs to be made clearer in the article.--J S Lundeen 10:27, 1 April 2006 (UTC)

What should be made clearer in my opinion is the fact that the Fourier theorem implies that the whole spectrum is actually phase-locked and that thus the bandwidth/coherence_time relationship can not be applied to natural light.

Anyway, is there a reference for the statement that white light has a coherence time of only 10 periods or so? Is this merely a theoretical figure based on the spectral width of white light or has it been measured? And if the latter, how does one know that the coherence time is actually not determined by the length of the individual light pulses (as given by the individual atomic emissions) rather than the combined bandwidth. I found actually a reference where the coherence length of white light has been measured to be about 200 micrometers, which is subtantially more than the generally quoted value of a few micrometers (see http://www.iop.org/EJ/abstract/0143-0807/24/4/363 ).

Thomas

Hi Thomas. You are still misunderstanding this. The coherence time has NOTHING to do with the phase between different frequencies. It can always be applied (including natural light). The bandwidth-coherence time relationship involves the fourier transform of the "power spectrum" (the absolute squared of the E-field spectrum). The power spectrum is always real and positive - there is no phase in it. Let me reiterate - the coherence time only tells you about the spectrum of the light it does not tell you about its time-duration. As for the white-light coherence - I have measured it personally - as have many physics undergrads. The reference you give measures the coherence time of white light transmitted through a filter - in other words, after the filter it is no longer white, it has a smaller bandwidth and thus should have a longer coherence time. Time-duration is related to second-order coherence as measured in an autocorrelator.--J S Lundeen 18:31, 4 April 2006 (UTC)

I find it somewhat paradoxical when you are saying that the coherence time has nothing to do with the phase, when in fact coherence time is defined as the time over which a a predictable phase relationship is maintained.

Consider for instance a light source which emits individual light pulses of a number of different frequencies such that the pulses do not overlap at all but arrive at the measuring instrument one by one. Let's assume each of these pulses has a length of let's say 10^-8 sec. So even if the frequencies span the whole of the visible spectrum, it would be then clearly incorrect to say that the coherence time is 10^-14 sec when in fact each pulse maintains the phase for 10^-8 sec (and one should be able to easily demonstrate this for instance by producing a diffraction pattern at a slit; what you would simply observe here is all the diffraction patterns for each corresponding color at once, whereas with a coherence time of 10^-14 sec you should obviously not see any diffraction pattern at all).

Thomas

I thank you thomas for pointing out some the things that need to be made clearer in the article. There are different types of coherence - temporal coherence (and the coherence time) refers to the phase relationship (or correlation) between different times of the wave. This is a different phase than the one that appears between different frequencies in the wave - this type of coherence is called spectral coherence (or chromatic coherence). It is the spectral coherence that relates to the time duration of the light - light with little spectral coherence will have a longer duration than light with perfect spectral coherence. To reiterate, I didn't say the "coherence time" had nothing to do with phase" - I said it has nothing to do with the phase between frequencies (the spectral phase).

I can't address your example because I don't really understand what situation you are trying describe. I will try to change the article soon so that it is clearer. Hopefully, the next version will clear up some misunderstandings for you.--J S Lundeen 19:31, 5 April 2006 (UTC)

So the Fourier theorem actually provides a relationship between the spectral bandwidth and the *chromatic* coherence rather than the phase coherence. I think this is a very important point (as the example in my previous post above should make clear).

Thomas

In the meanwhile, I have treated the issue in more detail on my webpage http://www.physicsmyths.org.uk/fourier.htm ,which I hope further clarifies the topic( by all means, feel free to improve the Wikipedia article even further in this sense).

Thomas Smid 10:52, 9 February 2007 (UTC)

Figures

The figures don't display properly!!!

Things this article doesn't explain

Just imagine the sort of questions that a high school student might ask. How can a small slit in front of a light source produce coherence? Consider the source behind the slit. Each atom in the light source is working away independently and so photons arrive at the slit with every possible phase. How does the slit put them in phase? Somehow the photons get in step. What is the process? The width of the slit has to comparable with the wavelength of light. If so, how wide? Is the gap in the middle still big enough for most light to get through unaffected?

Consider the colours in a film of gasoline on water. One photon that was in phase with another interfers with another after reflecting off a different surface. This should only work if a significant proportion of the photons were in phase. How can the sun be considered as a coherent source in this instance? No coherence can occurs because the photons are emitted thousands of miles apart and so they will arrive with totally random phases. I guess the coloured bands are produced because the interference happens “within” the same photon ie it takes both paths.

The problem with many Wikipedia articles on physics is that they would put off any high school student who just wanted a clear explanation. It does not have to be over-simplified. Mathematics is all very well for the purists, but should always be kept to the end of an article, long after the hand-waving explanations. Please just think about the audience when you are writing. JMcC 10:03, 24 May 2006 (UTC)

Definition

I´ll try later to read all the previous comments. Anyway, the definition of coherence (the first line of the article) should not be based on interference considering it should be able to explain such phenomenon. And reading the interference article one finds that in the first sentences, it is kind of defined based on the concept of coherence, making the definitions circular and thus unsatisfactory. The article is quite confusing.--Wikiwert 04:36, 18 August 2007 (UTC)

This article is horrible

I'm having real difficulty reading this article, and I'm familiar with the field. It simply assumes too much and many symbols used in the presented inline equations are not defined. —Preceding unsigned comment added by 58.107.215.254 (talk) 05:29, 23 October 2007 (UTC)

Figure 10 is quite wrong

Take a look at figure 10 in the article. The different colors are supposed to represent different frequencies, but they all have the same period! (And for some reason different amplitudes...) This would be extremely confusing to a new student. In general, I believe all of the figures need some work. I agree with the previous comments about the misleading nature of the "squiggly snakes". If only I had the time to fix it myself...